House Republicans and the White House are working furiously to shore up enough votes on their health care bill even as the prospect of passing a bill in that chamber looks daunting.

Vice President Mike Pence spent the morning on Capitol Hill for the second time in as many days, working to persuade hold-outs to support the measure. And President Donald Trump has also been speaking with individual members urging them to support the bill.

Republicans lost the support of a high-profile Republican Tuesday when Rep. Fred Upton of Michigan, the former chairman of the House Energy and Commerce Committee and ally to leadership, came out against the bill in an interview with a local radio station.

"I've supported the practice of not allowing pre-existing illnesses to be discriminated against from the very get-go. This amendment torpedoes that," Upton told WHTC radio.

And Rep. Billy Long of Missouri said he told the president in a phone conversation that he's opposed.

"I like the president a lot. I think he has done a very good job," Long said Tuesday. "I just think that some of the things we have been trying to do in the House haven't worked and I think the president needs to lead. He needs to use more leadership and tell us in the House exactly what he wants done and let us go out and do it instead of fighting amongst ourselves."

Pence spent Tuesday morning in his office in the Capitol, meeting with some of the most vocal opponents to the bill and some who are undecided.

Rep. Charlie Dent, R-Pennsylvania, who has been ardently against the measure, emerged from the meeting unconvinced.

"I told him my concerns continue to be about Medicaid expansion not being soft on its landing," Dent said. "He knows my position."

Reps. Dave Reichert of Washington and Peter Roskam of Illinois both entered the meeting undecided and left saying their position was unchanged.

While 21 Republicans have come out against the bill, according to NBC News' count, there are at least 17 who are undecided. While leaders are trying to convince the no votes to change their mind, they are also focusing on those who are wavering, understanding they can't afford to lose any more.

Many of those inclined to oppose the revised bill are centrists who come from districts where they are at risk of losing re-election. Twelve of the 21 members who have said they're voting "no" are being targeted by the Democrats' campaign committee, and so are half of the members who have said they're undecided.

But Republican leaders are reaching out to members individually, hoping to convince them that the changes made to the bill that convinced the most ardent conservatives to support it don't actually gut coverage for pre-existing conditions. Leaders are also exploring ways to address their concerns to get them on board.

Rep. Lou Barletta of Pennsylvania said he was promised a vote on a bill that would attempt to combat fraud related to the tax credits offered in the health care bill.

"I think it will certainly ease the concerns for not only myself but many others," Barletta said.

An amendment by Rep. Tom MacArthur of New Jersey has helped to revive the health care bill by addressing some of the concerns of conservatives. It allows states to opt out of some insurance mandates, such as the requirement that benefits cover maternity care and emergency care.

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U.S. Speaker of the House Paul Ryan (R-WI) attends a press conference following a meeting of the House Republican caucus at the U.S. Capitol May 2, 2017 in Washington, DC.

Despite House Speaker Paul Ryan saying during a news conference Tuesday that Republican are " excited about this policy," not many Republicans are. For those who are voting yes, many are doing so reluctantly.

"I'm a 'yes' but not an enthusiastic 'yes,'" said Rep. Peter King, R-New York.

He said he's going to vote for it to "move the bill forward." He said the most recent changes to the bill have made it "worse," but he's confident the Senate will improve it.

Public polling has shown that the bill, called the American Health Care Act, is not popular. Half of all respondents said that they have "little or no" confidence that the Republican bill will make their health care better, according to a recent NBC News poll. And that is up from 34 percent in February.

Still, leadership allies are expressing confidence that they can pass the bill this week.

"We've been making important progress on this bill that actually repeals and replaces Obamacare and puts patients back in charge and lowers premiums in the health care marketplace that is failing in a very dismal way right now," said Rep. Steve Scalise, the member in charge of counting the votes.